You develop a new repellent for ticks. You would like to evaluate if it is effective at repelling ticks. You plan an experiment in which you will have some number (n_T) of volunteers apply the repellent and some number (n_C) of volunteers not apply the repellent. You will then have both groups of volunteers walk through a dense forest in Kentucky. After an hour of walking you will check each volunteer to determine if they have a tick present on them (a "success") or do not have a tick present on them (a "failure"). You hypothesize that _T< _C, where is the probability a volunteer has a tick on them after an hour of walking through the forest. You do preliminary experiment where you have 10 volunteers who have not applied the repellent walk through the forest. After an hour 7 have ticks on them. Using this preliminary data, conduct a simulation study (with 10,000) replications to determine the sample sizes required, n_Tand n_Cto test Ha: _T< _Cvs H₀: _{T C}if you plan on conducting a two-sample test for a difference in proportions with = 0.025. Assume that you must have equal sample sizes in each group.